Matematik Bölümü Yayın Koleksiyonu

Permanent URI for this collectionhttps://hdl.handle.net/20.500.12416/413

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Author: search.filters.author.Jarad, FahdHas files: No

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Now showing 1 - 10 of 327
  • Article
    Citation - WoS: 6
    Citation - Scopus: 6
    Modeling the Transmission Dynamics of Middle Eastern Respiratory Syndrome Coronavirus with the Impact of Media Coverage
    (Elsevier, 2021) Fatima, BiBi; Alqudah, Manar A.; Zaman, Gul; Jarad, Fahd; Abdeljawad, Thabet
    Middle East respiratory syndrome coronavirus has been persistent in the Middle East region since 2012. In this paper, we propose a deterministic mathematical model to investigate the effect of media coverage on the transmission and control of Middle Eastern respiratory syndrome coronavirus disease. In order to do this we develop model formulation. Basic reproduction number R-0 will be calculated from the model to assess the transmissibility of the (MERS-CoV). We discuss the existence of backward bifurcation for some range of parameters. We also show stability of the model to figure out the stability condition and impact of media coverage. We show a special case of the model for which the endemic equilibrium is globally asymptotically stable. Finally all the theoretical results will be verified with the help of numerical simulation for easy understanding.
  • Article
    Citation - WoS: 51
    Citation - Scopus: 66
    Existence and Uniqueness of Solutions to Fractional Differential Equations in the Frame of Generalized Caputo Fractional Derivatives
    (Springer, 2018) Gambo, Y. Y.; Ameen, R.; Jarad, Fahd; Abdeljawad, T.
    The generalized Caputo fractional derivative is a name attributed to the Caputo version of the generalized fractional derivative introduced in Jarad et al. (J. Nonlinear Sci. Appl. 10:2607-2619, 2017). Depending on the value of. in the limiting case, the generality of the derivative is that it gives birth to two different fractional derivatives. However, the existence and uniqueness of solutions to fractional differential equations with generalized Caputo fractional derivatives have not been proven. In this paper, Cauchy problems for differential equations with the above derivative in the space of continuously differentiable functions are studied. Nonlinear Volterra type integral equations of the second kind corresponding to the Cauchy problem are presented. Using Banach fixed point theorem, the existence and uniqueness of solution to the considered Cauchy problem is proven based on the results obtained.
  • Article
    Citation - WoS: 4
    Citation - Scopus: 4
    Fractional Vector Calculus in the Frame of a Generalized Caputo Fractional Derivative
    (Univ Politehnica Bucharest, Sci Bull, 2018) Jarad, Fahd; Gambo, Yusuf Ya'u; Baleanu, Dumitru; Jarad, Fahd; Baleanu, Dumitru; Abdeljawad, Thabet; Abdeljawad, Thabet; Matematik
    The authors in [1] recently introduced a new generalized fractional derivative on AC(y)(n)[a ,b] and C-y(n)[a, b], and defined their Caputo version. This derivative contains two parameters and reduces to the classical Caputo derivatives if one of these parameters tend to certain values. From here and after, by generalized Caputo fractional derivative, we refer to the Caputo version of the generalized fractional derivative. This paper studies the generalized Caputo fractional derivative and establishes the Fundamental Theorem of Fractional Calculus (FTFC) in the sense of this derivative. The fundamental results are used in establishing some vital theorems and then applied to vector calculus.
  • Article
    Citation - WoS: 2
    On Polya-Szego Type Inequalities Via K-Fractional Conformable Integrals
    (Univ Punjab, dept Mathematics, 2020) Rashid, Saima; Jarad, Fahd; Jarad, Fahd; Noor, Muhammad Aslam; Noor, Khalida Inayat; Safdar, Farhat; Matematik
    The studies of inequalities regarding the fractional differential and integral operators are considered to be essential because of their potential applications among researchers. This paper consigns to the generalizations of novel fractional integral inequalities. The Polya-Szego type variants are generalized by involving K-fractional conformable integrals (KFCI): This is the K-analogue of the fractional conformable integrals. We discuss the implications and other consequences of the K-fractional conformable fractional integrals.
  • Article
    Citation - Scopus: 7
    On the Discrete Laplace Transform
    (Cankaya University, 2019) Ameen, R.; Jarad, Fahd; Köse, H.; Jarad, F.; Matematik
    The objective of this paper is to introduce the discrete Laplace transform. Basic theorems related to this transformation are mentioned and the discrete Laplace transform of basic functions are given. © 2019, Cankaya University. All rights reserved.
  • Article
    Citation - WoS: 14
    Citation - Scopus: 19
    On the Discrete Sumudu Transform
    (Editura Acad Romane, 2012) Jarad, Fahd; Jarad, Fahd; Abdeljawad, Thabet; Bayram, Kamm; Abdeljawad, Thabet; Baleanu, Dumitru; Baleanu, Dumitru; Köse, Hasan; Ameen, Raad; Matematik
    In this paper, we define the Sumudu transform on an arbitrary time scale. Starting from this definition we define the discrete Sumudu transform. We prove the initial and final value problems and study the basic properties of this transform. We also present the discrete Sumudu transform of some basic functions.
  • Article
    Citation - Scopus: 5
    Chaos in New 2-D Discrete Mapping and Its Application in Optimization
    (InforMath Publishing Group, 2020) Bououden, R.; Jarad, Fahd; Abdelouahab, M.S.; Jarad, F.; Matematik
    In this paper, we propose a new map which is a combination of the Hénon and Lozi maps. We analyze the proposed map numerically and with the aid of bifurcation plots. On the other hand, and as an example of application of this new map, we are going to use it in the chaotic optimisation algorithm. To prove the efficiency of this map, we use numerical results thorought the paper. © 2020 InforMath Publishing Group
  • Article
    Citation - WoS: 38
    Citation - Scopus: 39
    On the Mittag-Leffler Stability of Q-Fractional Nonlinear Dynamical Systems
    (Editura Acad Romane, 2011) Jarad, Fahd; Jarad, Fahd; Abdeljawad, Thabet; Abdeljawad, Thabet; Gundogdu, Emrah; Baleanu, Dumitru; Baleanu, Dumitru; Matematik
    In this article, analogous to the definition of the exponential stability of ordinary dynamical systems and the Mittag-Leffler stability of the fractional dynamical systems, we consider the Mittag-Leffler stability for q-fractional nonlinear dynamical systems. The sufficient conditions for Mittag-Leffler stability of such dynamical systems within the framework of the q-fractional Caputo derivative are studied.
  • Article
    Citation - WoS: 121
    Citation - Scopus: 125
    On Cauchy Problems With Caputo Hadamard Fractional Derivatives
    (Eudoxus Press, Llc, 2016) Jarad, Fahd; Adjabi, Y.; Baleanu, Dumitru; Jarad, Fahd; Baleanu, D.; Abdeljawad, Thabet; Abdeljawad, T.; Matematik
    The current work is motivated by the so-called Caputo-type modification of the Hadamard or Caputo Hadamard fractional derivative discussed in [4]. The main aim of this paper is to study Cauchy problems for a differential equation with a left Caputo Hadamard fractional derivative in spaces of continuously differentiable functions. The equivalence of this problem to a nonlinear Volterra type integral equation of the second kind is shown. On the basis of the obtained results, the existence and uniqueness of the solution to the considered Cauchy problem is proved by using Banach's fixed point theorem. Finally, two examples are provided to explain the applications of the results.
  • Editorial
    A Special Issue in Honor of the 55th Birthday of Dumitru Baleanu
    (Cankaya University, 2019) Jarad, F.; Jarad, Fahd; Matematik